On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters only. Find the probability that a randomly chosen team member runs only long-distance or competes only in field events.

Question

Mathematics

Cortez

1 July, 18:29

On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters only. Find the probability that a randomly chosen team member runs only long-distance or competes only in field events.

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Antoine Welch · Answer 1

0.40

Step-by-step explanation:

Members who run only long distance = 8%

So, probability that a member will run only long distance = P (A) = 0.08

Members who compete only in field events = 32%

So, probability that a member will compete only in field events = P (B) 0.32

Members who are sprinters = 12%

So, probability that a member is sprinter = P (C) 0.12

We have to calculate the probability that a randomly chosen team member runs only long-distance or competes only in field events. i. e we have to find P (A or B). Since these events cannot occur at the same time, we can write:

P (A or B) = P (A) + P (B)

Using the values, we get:

P (A or B) = 0.08 + 0.32 = 0.40

Thus, the probability that a randomly chosen team member runs only long-distance or competes only in field events is 0.40